Chapter 32
Inductance
Quick Quiz 32.1
A coil with zero resistance has its ends labeled a and b. The
potential at a is higher than at b. Which of the following
could be consistent with this situation?
(a) The current is constant and is directed from a to b
(b) The current is constant and is directed from b to a
(c) The current is increasing and is directed from a to b
(d) The current is decreasing and is directed from a to b
(e) The current is increasing and is directed from b to a
(f) The current is decreasing and is directed from b to a
Quick Quiz 32.1
Answer: (d), (e). For the constant current in (a) and (b),
there is no potential difference across the resistanceless
inductor. In (c), if the current increases, the emf induced in
the inductor is in the opposite direction, from b to a, making
b higher in potential than a. Similarly, in (f), the decreasing
current induces an emf in the same direction as the current,
from b to a, again making the potential higher at b than a.
Quick Quiz 32.2a
The circuit in the figure below consists of a resistor, an
inductor, and an ideal battery with no internal resistance. At
the instant just after the switch is closed, across which
circuit element is the voltage equal to the emf of the battery?
(a) the resistor
(b) the inductor
(c) both the inductor and
resistor
Quick Quiz 32.2a
Answer: (b). As the switch is closed, there is no current, so
there is no voltage across the resistor.
Quick Quiz 32.2b
After a very long time, across which circuit element is the
voltage equal to the emf of the battery?
(a) the resistor
(b) the inductor
(c) both the inductor and
resistor.
Quick Quiz 32.2b
Answer: (a). After a long time, the current has reached its
final value, and the inductor has no further effect on the
circuit.
Quick Quiz 32.3
The circuit in the figure below includes a power source that
provides a sinusoidal voltage. Thus, the magnetic field in the
inductor is constantly changing. The inductor is a simple air-core
solenoid. The switch in the circuit is closed and the lightbulb
glows steadily. An iron rod is inserted into the interior of the
solenoid, which increases the magnitude of
the magnetic field in the solenoid.
As this happens, the brightness of
the lightbulb:
(a) increases
(b) decreases
(c) is unaffected
Quick Quiz 32.3
Answer: (b). When the iron rod is inserted into the solenoid,
the inductance of the coil increases. As a result, more
potential difference appears across the coil than before.
Consequently, less potential difference appears across the
bulb, so the bulb is dimmer.
Quick Quiz 32.4
Two circuits like the one shown in Figure 32.6 are identical
except for the value of L. In circuit A the inductance of the
inductor is LA, and in circuit B it is LB. Switch S is thrown to
position a at t = 0. At t = 10 s, the switch is thrown to position b.
The resulting time rates of change for the two currents are as
graphed in the figure
below. If we assume
that the time constant
of each circuit is much
less than 10 s, which
of the following is true?
(a) LA > LB
(b) LA < LB
(c) not enough
information to tell
Quick Quiz 32.4
Answer: (b). Figure 32.10 shows that circuit B has the
greater time constant because in this circuit it takes longer
for the current to reach its maximum value and then longer
for this current to decrease to zero after switch S2 is closed.
Equation 32.8 indicates that, for equal resistances RA and RB,
the condition B > A means that LA < LB.
Quick Quiz 32.5
You are performing an experiment that requires the highest
possible energy density in the interior of a very long
solenoid. Which of the following increases the energy
density? (More than one choice may be correct.)
(a) increasing the number of turns per unit length on the
solenoid
(b) increasing the cross-sectional area of the solenoid
(c) increasing only the length of the solenoid while keeping
the number of turns per unit length fixed
(d) increasing the current in the solenoid
Quick Quiz 32.5
Answer: (a), (d). Because the energy density depends on the
magnitude of the magnetic field, to increase the energy
density, we must increase the magnetic field. For a solenoid,
B = 0nI, where n is the number of turns per unit length. In
(a), we increase n to increase the magnetic field. In (b), the
change in cross-sectional area has no effect on the magnetic
field. In (c), increasing the length but keeping n fixed has no
effect on the magnetic field. Increasing the current in (d)
increases the magnetic field in the solenoid.
Quick Quiz 32.6
In the figure below, coil 1 is moved closer to coil 2, with the
orientation of both coils remaining fixed. Because of this
movement, the mutual induction of the two coils
(a) increases
(b) decreases
(c) is unaffected
Quick Quiz 32.6
Answer: (a). M12 increases because the magnetic flux
through coil 2 increases.
Quick Quiz 32.7
At an instant of time during the oscillations of an LC circuit,
the current is at its maximum value. At this instant, the
voltage across the capacitor
(a) is equal to that across the inductor
(b) is zero
(c) has its maximum value
(d) is impossible to determine
Quick Quiz 32.7
Answer: (b). If the current is at its maximum value, the
charge on the capacitor is zero.
Quick Quiz 32.8
At an instant of time during the oscillations of an LC circuit,
the current is momentarily zero. At this instant, the voltage
across the capacitor
(a) is equal to that across the inductor
(b) is zero
(c) has its maximum value
(d) is impossible to determine
Quick Quiz 32.8
Answer: (c). If the current is zero, this is the instant at which
the capacitor is fully charged and the current is about to
reverse direction.